The mobile phone video from inside a classroom at Santa Monica High School went viral late last week.

It showed Mark Black, a longtime teacher and wrestling coach, swatting at a student with his arms, grabbing the teenager by the thigh and then crashing into desks and the classroom wall as he tried to execute a takedown. Moments later, Black had the young man pinned to the ground.

District Superintendent Sandra Lyon called the incident "utterly alarming" and acted swiftly, placing the teacher on leave pending the outcome of an investigation. In a statement released hours after the fight, she called the teacher's use of physical restraint "unacceptable" and pledged that the Santa Monica-Malibu Unified School District would offer support to the student's family.

Irate parents flooded Lyon and school board members with letters, castigating the superintendent for pre-judging the popular teacher and fiercely defending Black, 60, for what some saw as an act of bravery. Thousands of people liked a "We Support Coach Black of Samohi" page on Facebook and signed a Change.org petition calling for the coach's reinstatement.

So Lyon issued a second statement over the weekend, acknowledging that her remarks about Black had "caused great anger" and apologising to the community.

On Monday, Santa Monica police announced the arrest of an 18-year-old and a 16-year-old in connection with the classroom scuffle and said they would seek battery charges against both students.

The investigation casts a different light on Black's physical altercation, which some supporters say was necessary to keep other students safe. One school board member said the incident arose from a conflict over drug use, which raises complicated questions about when and how school staffers should intervene when students pose a threat or break a rule.

"It's a huge controversy when teachers put their hands on students," school board member Oscar de la Torre said. "From me knowing Mr Black personally — he was a former teacher of mine — I know him to be a fair person. The school board is committed to conducting a thorough and fair investigation."

Police and jail records identified the 18-year-old as Blair Moore. He is due in court on Tuesday for arraignment, and police are asking that he be charged with threatening a school official, possession of a weapon — a box cutter — on a school campus and possession of marijuana on school grounds, in addition to the battery charge.

Police did not identify the 16-year-old.

De la Torre said other staffers were injured trying to break up the melee and at least one person sought medical attention.

Lyon did not return multiple phone messages seeking comment, but in a third statement Monday she defended her decision to place Black on paid administrative leave as "standard procedure." Black did not reply to an email seeking comment.

Darrell Goode, president of the Santa Monica-Venice branch of the National Association for the Advancement of Coloured People, voiced support for the superintendent's action. He said the recent event was particularly sensitive because of an incident about a year and a half ago in which an African American wrestler at the school was hazed by white teammates.

"They have security, so I'm not sure why a teacher would need to grab a student under any condition," Goode said. "It's just judgment. You call security and security calls police."

But Daniel Jacobs, 32, a 1999 Santa Monica High School graduate who runs a Silicon Valley start-up, was so upset by Lyon's initial statement that he started his own Change.org petition, which asks Lyon to apologise.

Jacobs said that when he saw the video, his reaction was that it captured Black "trying to neutralise a threat."

Jacobs said that whenever he returns to Santa Monica, he makes a point of visiting Black. "I've never met a better or more kindhearted man in my life."